Advertisements
Advertisements
प्रश्न
Study the two circuits shown in the figure below. The cells in the two circuits are identical to each other. The resistance of the load resistor R is the same in both circuits.
If the same current flows through the resistor R in both circuits, calculate the internal resistance of each cell in terms of the resistance of resistor R. Show your calculations.
उत्तर
Current I in load resistance R is given by the formula,
I = `"E"/("R"+"r")`;
where E is the emf of the cell,
r is the internal resistance of the cell.
In circuit 1, the cells are in series.
∴ Eeq = 2E and req = 2r
Current through R in circuit 1, I = `(2"E")/(("R"+2"r"))`
In circuit 2, the cells are in parallel.
∴ Eeq = E and req = `"r"/2`
Current through R in circuit 2, I = `"E"/(("R"+"r"/2))`
Since the current is the same in both circuits,
`(2"E")/ (("R"+2"r")) = "E"/(("R"+"r"/2))`
Solving, we get r = R
APPEARS IN
संबंधित प्रश्न
A cell of emf 'E' and internal resistance 'r' is connected across a variable resistor 'R'. Plot a graph showing variation of terminal voltage 'V' of the cell versus the current 'I'. Using the plot, show how the emf of the cell and its internal resistance can be determined.
A long straight current carrying wire passes normally through the centre of circular loop. If the current through the wire increases, will there be an induced emf in the loop? Justify.
A 10 V cell of negligible internal resistance is connected in parallel across a battery of emf 200 V and internal resistance 38 Ω as shown in the figure. Find the value of current in the circuit.
A cell of emf ‘E’ and internal resistance ‘r’ draws a current ‘I’. Write the relation between terminal voltage ‘V’ in terms of E, I and r ?
A rectangular conductor LMNO is placed in a uniform magnetic field of 0.5 T. The field is directed perpendicular to the plane of the conductor. When the arm MN of length of 20 cm is moved towards left with a velocity of 10 ms−1, calculate the emf induced in the arm. Given the resistance of the arm to be 5 Ω (assuming that other arms are of negligible resistance) find the value of the current in the arm.
Two cells of emf E1, E2 and internal resistance r1 and r2 respectively are connected in parallel as shown in the figure.
Deduce the expressions for
(1) the equivalent e.m.f of the combination
(2) the equivalent resistance of the combination, and
(3) the potential difference between the point A and B.
Can the potential difference across a battery be greater than its emf?
Do the electrodes in an electrolytic cell have fixed polarity like a battery?
Three cells, each of emf E but internal resistances 2r, 3r and 6r are connected in parallel across a resistor R.
Obtain expressions for (i) current flowing in the circuit, and (ii) the terminal potential differences across the equivalent cell.
